The princesses’ father, the Duke of York, decided not to attend the gathering after speaking to his ex-wife and close friend, Sarah Ferguson, according to a source.
The Buckingham Palace lunch is a private event for senior royals and their wider family who will not be attending Christmas celebrations at the King’s Norfolk home.
Members of the family pictured arriving at Buckingham Palace on Thursday included the King and Queen and the Duke and Duchess of Edinburgh.
Also attending were Lord Frederick Windsor, his wife Sophie Winkleman and their daughter Isabella; the Duke of Kent; Prince and Princess Michael of Kent; the Earl of St Andrews; Lady Marina Windsor and Lady Amelia Windsor; Timothy Taylor, Lady Helen Taylor, Estella and Eloise Taylor; Lady Margarita Armstrong-Jones; and Lord Downpatrick.
They were joined by Countess Mountbatten of Burma Penelope Knatchbull; James and Julia Ogilvy; Samuel Chatto; the Earl of Ulster and Lord Culloden; Flora and Timothy Vesterberg; Princess Alexandra; and Lady Davina Windsor.
Earlier this week, Prince Andrew pulled out of the meal as he continues to be dogged by his links to an alleged Chinese spy.
The King’s brother had already withdrawn from joining senior royals at Sandringham for the festive period.
It was previously revealed in a High Court hearing that alleged Chinese spy Yang Tengbo, who was banned from the UK, was said to have been a “close” confidant of Andrew.
Mr Yang, who was named after an anonymity order was lifted on Monday, has insisted it was “entirely untrue” to claim he was involved in espionage and that he has “done nothing wrong or unlawful”.
The businessman, previously referred to only as H6 in the legal case, was the founder-partner of the Chinese arm of the duke’s PitchPalace initiative, and twice visited Buckingham Palace in 2018 to meet with the late Queen’s second son.
He is also said to have entered St James’s Palace and Windsor Castle at Andrew’s invitation.
On Friday, the duke’s office said Andrew “ceased all contact” with the then-unnamed businessman when concerns were first raised about him.
Andrew met Mr Yang through “official channels” with “nothing of a sensitive nature ever discussed”, a statement said.